Bosznay, A. P. A gradient-type method to solve a system of quadratic equations. (English) Zbl 0531.65026 Z. Angew. Math. Mech. 63, No. 5, T340-T341 (1983). Summary: Let us consider the following system of quadratic equations \[ \sum^{n}_{j=1}a_{i,j}x_ j+\sum^{n}_{j,k=1}b_{i,j,k}x_ jx_ k+c_ i=0,\quad i=1,...,m. \] This system arises in an inverse eigenvalue problem of mechanics. Numerical tests show that classical methods fail numerically even in cases n,\(m\leq 5\) in the solution of the above system. In this lecture we show a special gradient-type method to solve this system. Numerical examples are also considered. MSC: 65H10 Numerical computation of solutions to systems of equations 65K05 Numerical mathematical programming methods 90C20 Quadratic programming Keywords:inverse eigenvalue problem; Numerical tests; gradient-type method; Numerical examples PDFBibTeX XMLCite \textit{A. P. Bosznay}, Z. Angew. Math. Mech. 63, T340--T341 (1983; Zbl 0531.65026) Full Text: DOI